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Answers to Eiffel Tower and other puzzles

1. For solving this problem, we use the property of similar figures that the volumes of similar figures are to one another as the cubes of their heights, provided both are made of the same material.
Therefore, here the volume of the model is 1/8,000,000 of the volume of the tower. Hence, the height of the model must be (1/8,000,000)^1/3 = 1/200 times shorter. The height of the tower is, therefore, 300/200 = 1.5 m.

2. The mother should get half of what the son gets and double if what the daughter gets. Let the daughter's share be n.Therefore, the mother's share is 2n and the son's share is 4n. Hence the daughter, son and mother get 1/7th, 4/7th and 2/7th of the man's property.

3. Let n be the number of days in which he typed. Then, he typed 45000n words.

Therefore the total number of words = 45000n+7000+3000
Average rate was 40000 words a day for n+2 days.
Now, 40000(n+2) = 45000n + 10000
n = 14
Hence, the total number of days = 14+2 = 16

4. Let C.P.= x y , therefore S.P.= y x

(10y + x) - (10x + y) = 10x + x + y
2y = 5x
For y to be a single digit, x=2 and y=5. Therefore C.P.=25 and S.P.=52.
Profit = 52 - 25 = 27.

- Vinaya Kini
(Epsilon)